ANALEX CORPORATION

Exhibit 4.1

ANALEX CORPORATION

AMENDMENT TO CERTIFICATE OF DESIGNATIONS,

POWERS, PREFERENCES AND RIGHTS

OF THE SERIES A CONVERTIBLE PREFERRED STOCK BY RESOLUTION OF THE

BOARD OF DIRECTORS

I, Sterling E. Phillips, Jr., Chief Executive Officer of Analex Corporation (the “Corporation”), organized and existing under the laws of the State of Delaware, pursuant to the provisions of Section 151 of the General Corporation Law of the State of Delaware (“DGCL”), do hereby certify that pursuant to the authority expressly vested in the Board of Directors of the Corporation by the Certificate of Incorporation, the Board of Directors duly adopted the following resolutions amending the Certificate of Designations, Powers, Preferences and Rights of the Series A Convertible Preferred Stock (the “Certificate of Designations”), and these resolutions were approved by the holders of the requisite number of outstanding shares of Series A Convertible Preferred Stock in accordance with Section 151 of the DGCL and the Certificate of Designations:

NOW, THEREFORE, BE IT RESOLVED:

FIRST: That Section 7 of the Certificate of Designations be amended in its entirety to read as follows:

‘Section 7. Protective Provisions.

(a) So long as at least 50% of the shares of Series A Preferred Stock issued at the Series A Closing remain outstanding (as adjusted for any stock splits, stock dividends, combinations, recapitalizations involving equity of the Corporation, reclassifications of other similar events involving a change with respect to the Series A Preferred Stock), the Corporation shall not, without first obtaining the written consent of the holders of at least a majority of the then outstanding shares of Series A Preferred Stock voting as a separate class:

(i) increase or decrease the total number of authorized shares of Series A Preferred Stock the authorized shares of Common Stock reserved for issuance upon conversion of the Series A Preferred Stock (except as otherwise required by the Charter or the Certificate of Designations);

(ii) alter, amend or repeal the Charter or the Corporation’s bylaws, so as to affect adversely the voting powers, preferences or other rights, including, without limitation, the liquidation preferences, dividend rights, conversion rights, redemption rights or any reduction in the stated value of the Series A Preferred Stock;

(iii) following the expiration of the Corporation Option and except for the issuance of any subordinated debt in an amount not to exceed $3,000,000, issue any

securities, or securities that are convertible into securities, ranking senior to or pari passu with the Series A Preferred Stock but junior to the Series B Preferred Stock, with respect to voting, dividend, liquidation or redemption rights; or

(iv) issue any securities having an initial per share purchase price that is less than the Conversion Price (as adjusted for any stock splits, stock dividends, combinations, recapitalizations involving equity of the Corporation, reclassifications of other similar events involving a change with respect to the Series A Preferred Stock) other than Anti-Dilution Excluded Securities.

(b) So long as at least 50% of the shares of Series A Preferred Stock issued at the Series A Closing (as adjusted for any stock splits, stock dividends, combinations, recapitalizations involving equity of the Corporation, reclassifications of other similar events involving a change with respect to such Series A Preferred Stock) or, if the Corporation has failed to comply with its obligations to redeem the shares of Series A Preferred Stock in accordance with Section 11, so long as any shares of Series A Preferred Stock issued at the Series A Closing issued pursuant to the Note Purchase Agreement remain outstanding, the Corporation shall not, without first obtaining the written consent of the holders of at least a majority of the then outstanding shares of Series A Preferred Stock voting as a separate class:

(i) merge or consolidate with one or more entities or sell all or substantially all of the capital stock or assets of the Corporation;

(ii) following the expiration of the Corporation Option, make an acquisition or series of related acquisitions for consideration aggregating more than $10,000,000 in value;

(iii) declare or pay any dividends or distributions on the capital stock of the Corporation, except for dividends and distributions paid on the Series A Preferred Stock in accordance with the Charter and the Series B Preferred Stock in accordance with the Series B Certificate of Designations;

(iv) voluntarily liquidate or dissolve, recapitalize or reorganize the Corporation;

(v) borrow funds (in one or a series of related borrowings) in an amount aggregating more than $3,000,000 other than revolving lines of credit provided by lenders based upon the Corporation’s accounts receivable;

(vi) repurchase or repay any of the Corporation’s indebtedness prior to the stated maturity of any such indebtedness other than the Series B Notes;

(vii) redeem or purchase any of the capital stock of the Corporation, except (x) repurchases of employee Common Stock upon termination of employment pursuant to employment agreements in effect at the time of the Series A Closing,

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(y) redemption of the Series A Preferred Stock as contemplated by the Certificate of Designations and (z) redemption of the Series B Preferred Stock as contemplated by the Series B Certificate of Designations;

(viii) increase or decrease the number of members of the Board, other than as permitted in the Stockholders’ Voting Agreement; or

(ix) elect, appoint or remove the Chief Executive Officer, Chief Financial Officer, President or Chief Operating Officer of the Corporation.’

SECOND: That Section 9 of the Certificate of Designations be amended in its entirety to read as follows:

‘Section 9. Preemptive Rights.

Each holder of Series A Preferred Stock or debt or equity of the Corporation that is convertible into shares of Series A Preferred Stock shall be entitled to purchase its pro rata share (calculated by multiplying the number of securities issued in such equity offering including those issued pursuant this Section 9 by a fraction, the numerator of which is the number of shares of Common Stock held by such holder on a Fully Diluted Basis and the denominator of which is the number of shares of Common Stock held by all such holders of securities of the Corporation on a Fully Diluted Basis) of any future private equity offering (including, without limitation, any offering of convertible debt) by the Corporation, except for the Preemptive Rights Excluded Securities.’

THIRD: That Section 11 of the Certificate of Designations be amended in its entirety to read as follows:

‘Section 11. Redemption Rights. The record Holders of the Series A Preferred Stock shall have redemption rights as follows:

(a) Subject to Section 11(b) below, the Series A Preferred Stock shall be subject to redemption, at the option of the holders of a majority of the then outstanding shares of Series A Preferred Stock at any time after the Series B Redemption Date, in four equal quarterly installments, with the first installment being made within sixty (60) days of the date of exercise of such option and the last installment on the date that is 9 months thereafter, in whole or in part, at a per share redemption price equal to the Series A Original Issue Price (as adjusted for any stock splits, stock dividends, combinations, recapitalizations involving equity securities of the Corporation, reclassifications of other similar events involving a change with respect to the Series A Preferred Stock) per share plus any accrued but unpaid dividends, payable in immediately available funds.

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(b) The funds legally available to the Corporation for the payment of the redemption price of Series A Preferred Stock and Series B Preferred Stock shall be used first to pay the redemption price of Series B Preferred Stock on the dates established for redemption pursuant to Section 11(a) and the Corporation shall not be required to use such funds to pay the redemption price of Series A Preferred Stock unless the Corporation has paid, or reserved funds sufficient to pay, the entire redemption price of Series B Preferred Stock. If the funds legally available to the Corporation for the payment of the redemption price of the Series A Preferred Stock are not sufficient to redeem all of the shares of the Series A Preferred Stock required to be redeemed on any date, such funds shall be used to redeem the number of shares of Series A Preferred Stock which may be redeemed from such amount on a pro rata basis. If, at the end of each calendar quarter, thereafter (or more often than quarterly at the option of the Corporation), additional funds become available for the redemption of additional shares of Series A Preferred Stock required to be so redeemed, the Corporation shall (x) first, immediately use such funds to redeem shares of Series B Preferred Stock until such time as all of the shares of Series B Preferred Stock required to be redeemed pursuant to Section 12 of the Series B Certificate of Designations have been redeemed and (y) thereafter, use such funds to redeem shares of Series A Preferred Stock until such time as all of the shares of Series A Preferred Stock required to be redeemed pursuant to this Section 11 have been redeemed.

(c) If, on the dates established for redemption pursuant to Section 11(a), all of the shares of Series A Preferred Stock to be redeemed on each such date are not redeemed in full, all rights in respect of such shares of Series A Preferred Stock that have not been redeemed, including the right to receive the applicable redemption price, plus accrued and unpaid dividends, shall continue to be outstanding as evidenced by the certificates representing such shares. The exercise by the Holders of the option to redeem any shares of Series A Preferred Stock which were not redeemed on the dates established for redemption pursuant to Section 11(a), may be rescinded by such Holders at any time following the date established for such redemption by written notice to the Corporation. All shares of Series A Preferred Stock redeemed pursuant to Section 11(a) shall be retired and shall be restored to the status of authorized and unissued shares of Preferred Stock, without designation as to series or class and may thereafter be reissued, subject to compliance with the terms hereof, as shares of any series of Preferred Stock other than shares of Series A Preferred Stock.

(d) The Holders shall have the right, but not the obligation, to pursue all remedies available to them at law or in equity and shall have the right to designate additional members to the Board such that the directors designated by such Holders constitute a majority of the members of the Board if the Corporation is unable to effect any such quarterly redemption installment for a period of nine (9) consecutive months after such installment was required to be paid pursuant to Section 11(a) hereof; provided, that if any such installment remains unpaid for a period of nine (9) consecutive months after such installment was required to be paid, such Holders shall be entitled to such increased Board representation unless all such installments that are then past due are paid; provided, however, that the Holders shall not have any right to designate additional members to the Board pursuant to this Section 11(d) during any time that the holders of Series B Preferred Stock have exercised their rights to designate

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additional members to the Board pursuant to Section 12(d) of the Series B Certificate of Designations. Such additional members of the Board shall be designated and elected in accordance with the provisions of Section 2.1 of the Stockholders’ Voting Agreement.’

FOURTH: That the following definitions in Section 12 of the Certificate of Designations be amended in their entirety to read as follows:

‘“Senior Indebtedness” means the indebtedness of the Corporation under that certain Amended and Restated Credit Agreement dated on or about the date hereof, as amended, by and between the Corporation and Bank of America, N.A. and any other Senior Indebtedness as such term is defined in the Note Purchase Agreement.

“Stockholders’ Voting Agreement” means that certain Amended and Restated Stockholders’ Voting Agreement, dated on or about the date hereof, between the Corporation and the investors named therein.’

FIFTH: That the following definitions be included, in the appropriate alphabetical order, in Section 12 of the Certificate of Designations:

‘“Corporation Option” means the option of the Corporation for the period of 12 calendar months following the Issue Date to require each purchaser named in the Series B Purchase Agreement to purchase either additional Series B Notes or additional shares of Series B Preferred Stock, and in each case, warrants of the Corporation for an aggregate purchase price not to exceed $20,000,000, all in accordance with the Series B Purchase Agreement.

“Issue Date” means the earlier of (x) the date of the initial conversion of any Series B Notes or (y) the date of the initial issuance of any Series B Preferred Stock, as the case may be.

“Series B Certificate of Designations” means that certain Certificate of Designations, Powers, Preferences and Rights of the Series B Convertible Preferred Stock of the Corporation, dated May 27, 2004, as amended.

“Series B Notes” means those certain secured senior subordinated convertible promissory notes issued by the Corporation pursuant to the Series B Purchase Agreement.

“Series B Preferred Stock” means the Series B Convertible Preferred Stock, par value $.02 per share, of the Corporation.

“Series B Purchase Agreement” means that certain Purchase Agreement, dated on or about the date hereof, between the Corporation and the purchasers named therein.

“Series B Redemption Date” means the date that is any time after the fourth anniversary of the Issue Date whereupon the Series B Preferred Stock shall be subject to redemption.’

Signature on following page.

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IN WITNESS WHEREOF, the Corporation has caused this Amendment to be duly executed on its behalf by its Chief Executive Officer this 27th day of May, 2004.